Lens Maker Equation Calculator

The calculator uses the comprehensive lensmaker's formula that accounts for both thin and thick lenses. The mathematical relationship is expressed as: 1/f = (n - 1) * (1/R1 - 1/R2 + ((n - 1) * t) / (n * R1 * R2)), where f represents the focal length, n is the refractive index of the lens material, R1 and R2 are the radii of curvature for the first and second lens surfaces, and t is the central thickness of the lens.

Consider designing a thick biconvex lens made of crown glass. Let the refractive index (n) be 1.5, the thickness (t) be 0.02 meters, the radius of the first surface (R1) be 0.1 meters, and the radius of the second surface (R2) be -0.1 meters. Plugging these numbers into the formula: 1/f = (1.5 - 1) * (1/0.1 - 1/(-0.1) + ((1.5 - 1) * 0.02) / (1.5 * 0.1 * -0.1)). This evaluates to 1/f = 0.5 * (10 + 10 + (0.5 * 0.02) / (-0.015)), which simplifies to 1/f = 0.5 * (20 - 0.667) = 9.667 m^-1. Inverting this yields a focal length (f) of approximately 0.103 meters.

Always pay close attention to sign conventions when inputting radii of curvature; a surface curving away from the light source is typically positive, while one curving toward it is negative. Ensure your units for thickness and radius match consistently (e.g., all in meters or all in centimeters). Lastly, remember that extreme thicknesses can introduce spherical aberrations that simple thin-lens approximations fail to capture.